Question

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which graph displays the data best? explain.
2 7 3 3 10 3 15 7 5 9 9 13
7 10 11 1 3 12 4 6 3 2 10 15 14
create a histogram with 5 classes. choose the correct graph below.

Explanation:

Step1: Count data frequency

First, count the frequency of each data - value in the set: 2, 7, 3, 3, 10, 3, 15, 7, 5, 9, 9, 13, 9, 7, 10, 11, 1, 3, 12, 4, 6, 3, 2, 10, 15, 14.

Step2: Determine class intervals for 5 - class histogram

Find the range of the data. The minimum value is 1 and the maximum value is 15. The range \(R=15 - 1=14\). For 5 classes, the class - width \(w=\frac{14}{5}=2.8\), we can round it up to 3. The class intervals are: 1 - 3, 4 - 6, 7 - 9, 10 - 12, 13 - 15.

Step3: Calculate frequencies for each class

For the class 1 - 3: There are 8 values (1, 2, 2, 3, 3, 3, 3, 3).
For the class 4 - 6: There are 3 values (4, 5, 6).
For the class 7 - 9: There are 6 values (7, 7, 7, 9, 9, 9).
For the class 10 - 12: There are 4 values (10, 10, 10, 11, 12).
For the class 13 - 15: There are 4 values (13, 14, 15, 15).

Step4: Match with graphs

Based on the above - calculated frequencies for each class, match with the given graphs.

Answer:

Without seeing the actual graphs' details, we can't choose the exact correct option. But the correct graph should have the following frequencies for the classes 1 - 3, 4 - 6, 7 - 9, 10 - 12, 13 - 15: 8, 3, 6, 4, 4 respectively for the y - axis (frequency) and the appropriate class intervals on the x - axis.